TSTP Solution File: SET762+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:25:34 EDT 2022

% Result   : Theorem 0.21s 0.54s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   40 (  11 unt;   0 def)
%            Number of atoms       :  109 (   1 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  112 (  43   ~;  29   |;  25   &)
%                                         (   6 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   90 (  73   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f209,plain,
    $false,
    inference(subsumption_resolution,[],[f208,f185]) ).

fof(f185,plain,
    ~ equal_set(sF12,empty_set),
    inference(definition_folding,[],[f172,f184]) ).

fof(f184,plain,
    sF12 = image2(sK8,empty_set),
    introduced(function_definition,[]) ).

fof(f172,plain,
    ~ equal_set(image2(sK8,empty_set),empty_set),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ( maps(sK8,sK9,sK10)
    & ~ equal_set(image2(sK8,empty_set),empty_set) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f119,f120]) ).

fof(f120,plain,
    ( ? [X0,X1,X2] :
        ( maps(X0,X1,X2)
        & ~ equal_set(image2(X0,empty_set),empty_set) )
   => ( maps(sK8,sK9,sK10)
      & ~ equal_set(image2(sK8,empty_set),empty_set) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ? [X0,X1,X2] :
      ( maps(X0,X1,X2)
      & ~ equal_set(image2(X0,empty_set),empty_set) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ? [X1,X0,X2] :
      ( maps(X1,X0,X2)
      & ~ equal_set(image2(X1,empty_set),empty_set) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,plain,
    ~ ! [X1,X2,X0] :
        ( maps(X1,X0,X2)
       => equal_set(image2(X1,empty_set),empty_set) ),
    inference(rectify,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ! [X0,X5,X1] :
        ( maps(X5,X0,X1)
       => equal_set(image2(X5,empty_set),empty_set) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ! [X0,X5,X1] :
      ( maps(X5,X0,X1)
     => equal_set(image2(X5,empty_set),empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa12) ).

fof(f208,plain,
    equal_set(sF12,empty_set),
    inference(resolution,[],[f193,f202]) ).

fof(f202,plain,
    ! [X0] : subset(sF12,X0),
    inference(resolution,[],[f201,f168]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( member(sK7(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( member(sK7(X0,X1),X1)
          & ~ member(sK7(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f114,f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & ~ member(X3,X0) )
     => ( member(sK7(X0,X1),X1)
        & ~ member(sK7(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( member(X2,X1)
            & ~ member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ member(X2,X1)
          | member(X2,X0) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f201,plain,
    ! [X0] : ~ member(X0,sF12),
    inference(subsumption_resolution,[],[f200,f177]) ).

fof(f177,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f200,plain,
    ! [X0] :
      ( member(sK4(sK8,X0,empty_set),empty_set)
      | ~ member(X0,sF12) ),
    inference(superposition,[],[f154,f184]) ).

fof(f154,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,image2(X0,X2))
      | member(sK4(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ( ( member(sK4(X0,X1,X2),X2)
          & apply(X0,sK4(X0,X1,X2),X1) )
        | ~ member(X1,image2(X0,X2)) )
      & ( member(X1,image2(X0,X2))
        | ! [X4] :
            ( ~ member(X4,X2)
            | ~ apply(X0,X4,X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f96,f97]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( member(X3,X2)
          & apply(X0,X3,X1) )
     => ( member(sK4(X0,X1,X2),X2)
        & apply(X0,sK4(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( member(X3,X2)
            & apply(X0,X3,X1) )
        | ~ member(X1,image2(X0,X2)) )
      & ( member(X1,image2(X0,X2))
        | ! [X4] :
            ( ~ member(X4,X2)
            | ~ apply(X0,X4,X1) ) ) ),
    inference(rectify,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( member(X3,X2)
            & apply(X0,X3,X1) )
        | ~ member(X1,image2(X0,X2)) )
      & ( member(X1,image2(X0,X2))
        | ! [X3] :
            ( ~ member(X3,X2)
            | ~ apply(X0,X3,X1) ) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( member(X3,X2)
          & apply(X0,X3,X1) )
    <=> member(X1,image2(X0,X2)) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X5,X4,X0] :
      ( ? [X2] :
          ( apply(X5,X2,X4)
          & member(X2,X0) )
    <=> member(X4,image2(X5,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).

fof(f193,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | equal_set(X0,empty_set) ),
    inference(resolution,[],[f143,f188]) ).

fof(f188,plain,
    ! [X1] : subset(empty_set,X1),
    inference(resolution,[],[f168,f177]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | equal_set(X0,X1) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
    <=> equal_set(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:33:21 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.21/0.46  % (13432)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.46  % (13440)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.47  % (13432)Instruction limit reached!
% 0.21/0.47  % (13432)------------------------------
% 0.21/0.47  % (13432)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.47  % (13432)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.47  % (13432)Termination reason: Unknown
% 0.21/0.47  % (13432)Termination phase: Blocked clause elimination
% 0.21/0.47  
% 0.21/0.47  % (13432)Memory used [KB]: 1023
% 0.21/0.47  % (13432)Time elapsed: 0.005 s
% 0.21/0.47  % (13432)Instructions burned: 3 (million)
% 0.21/0.47  % (13432)------------------------------
% 0.21/0.47  % (13432)------------------------------
% 0.21/0.53  % (13448)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.53  % (13425)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.53  % (13452)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.53  % (13424)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.53  % (13452)First to succeed.
% 0.21/0.53  % (13450)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.53  % (13446)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.53  % (13428)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53  % (13426)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.53  TRYING [1]
% 0.21/0.53  TRYING [2]
% 0.21/0.53  % (13427)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53  % (13428)Also succeeded, but the first one will report.
% 0.21/0.54  % (13452)Refutation found. Thanks to Tanya!
% 0.21/0.54  % SZS status Theorem for theBenchmark
% 0.21/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54  % (13452)------------------------------
% 0.21/0.54  % (13452)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (13452)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (13452)Termination reason: Refutation
% 0.21/0.54  
% 0.21/0.54  % (13452)Memory used [KB]: 5500
% 0.21/0.54  % (13452)Time elapsed: 0.139 s
% 0.21/0.54  % (13452)Instructions burned: 5 (million)
% 0.21/0.54  % (13452)------------------------------
% 0.21/0.54  % (13452)------------------------------
% 0.21/0.54  % (13423)Success in time 0.184 s
%------------------------------------------------------------------------------